# Multicontinuum Wave Propagation in a Laminated Beam with Contrasting Stiffness and Density of Layers

## Abstract

The wave equation in a thin laminated beam with contrasting stiffness and density of layers is considered. The problem contains two parameters: ε is a geometric small parameter (the ratio of the diameter and its characteristic longitudinal size) and ω is a physical large parameter (the ratio of stiffness and densities of alternating layers). The asymptotic behavior of the solution depends on the combination of parameters ε{sup 2}ω. If this value is small, then the limit model is the standard homogenized one-dimensional wave equation. On the contrary, if ε{sup 2}ω is not small, then the limit model is presented by the so-called multicontinuum model, i.e., multiple one-dimensional wave equations, coupled or noncoupled and “co-existing” at every point. The proof of these results uses the milticomponent homogenization method.

- Authors:

- University of Lyon Institute Camille Jordan UMR CNRS 5208 and SFR MODMAD FED 4169 (France)

- Publication Date:

- OSTI Identifier:
- 22773946

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 232; Journal Issue: 4; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; DENSITY; FLEXIBILITY; GEOMETRY; HOMOGENIZATION METHODS; LAYERS; ONE-DIMENSIONAL CALCULATIONS; SUPPORTS; WAVE EQUATIONS; WAVE PROPAGATION

### Citation Formats

```
Panasenko, G. P., E-mail: Grigory.Panasenko@univ-st-etienne.fr.
```*Multicontinuum Wave Propagation in a Laminated Beam with Contrasting Stiffness and Density of Layers*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3889-7.

```
Panasenko, G. P., E-mail: Grigory.Panasenko@univ-st-etienne.fr.
```*Multicontinuum Wave Propagation in a Laminated Beam with Contrasting Stiffness and Density of Layers*. United States. doi:10.1007/S10958-018-3889-7.

```
Panasenko, G. P., E-mail: Grigory.Panasenko@univ-st-etienne.fr. Sun .
"Multicontinuum Wave Propagation in a Laminated Beam with Contrasting Stiffness and Density of Layers". United States. doi:10.1007/S10958-018-3889-7.
```

```
@article{osti_22773946,
```

title = {Multicontinuum Wave Propagation in a Laminated Beam with Contrasting Stiffness and Density of Layers},

author = {Panasenko, G. P., E-mail: Grigory.Panasenko@univ-st-etienne.fr},

abstractNote = {The wave equation in a thin laminated beam with contrasting stiffness and density of layers is considered. The problem contains two parameters: ε is a geometric small parameter (the ratio of the diameter and its characteristic longitudinal size) and ω is a physical large parameter (the ratio of stiffness and densities of alternating layers). The asymptotic behavior of the solution depends on the combination of parameters ε{sup 2}ω. If this value is small, then the limit model is the standard homogenized one-dimensional wave equation. On the contrary, if ε{sup 2}ω is not small, then the limit model is presented by the so-called multicontinuum model, i.e., multiple one-dimensional wave equations, coupled or noncoupled and “co-existing” at every point. The proof of these results uses the milticomponent homogenization method.},

doi = {10.1007/S10958-018-3889-7},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 4,

volume = 232,

place = {United States},

year = {2018},

month = {7}

}